Under what circumstances can a gear with an overheated bearing be allowed to operate?

Operating a gear with an overheated bearing is generally not advisable. However, it may be permissible under extreme circumstances, such as when the gear is critical to operations—often referred to in military context as "GQ" or general quarters. In such situations, allowing it to continue operating, despite the risk, might be necessary to maintain functionality and could be justified if the immediate need outweighs potential damage or safety concerns.

In the context of this decision, it's important to consider the potential consequences, such as the risk of failure or further damage to the equipment and the safety of personnel. Even in extreme circumstances, strict monitoring and a plan for expeditious repair or replacement should be in place to minimize adverse impacts on operations and equipment integrity.